# Math Help - function composition problem

1. ## function composition problem

Let h be defined as $h(x) = \sqrt{\sqrt{(x-3-9)}}.$Express h as a composition $f \circ g$. Identify f and g and state the domain and range of each of h, f and g.

Thanks guys.

2. Are you sure about the argument under the radical? It seems a little odd.

Actually, x - 3 - 3 would make it more fun.

Anyway, try $f(x) = \sqrt{x}$ and $g(x) = x - 3 - 9$. This gives f(f(g(x))) = h(x). Or we could have r(x) = x - 3 and get f(f(g(g(g(g(x)))))). Okay, I'm having too much fun.

3. hey sorry bout the late reply..internet was down after moving house

its meant to be

$h(x) = \sqrt{\sqrt{(x-3}-9)}.$

cheers

4. Originally Posted by smplease
hey sorry bout the late reply..internet was down after moving house

its meant to be

$h(x) = \sqrt{\sqrt{(x-3}-9)}.$

cheers
One obvious possibility is $f(x) = \sqrt{x}$ and $g(x) = \sqrt{x - 3} - 9$. I hope you see why.

There is another possibility, left for you to find.